Medical reporting practice Medico-Legal Consultancy (MLC) was scheduled to float on the Ofex market yesterday.
It had planned to trade up to 10% of its shares giving it an expected market capitalisation of about £7.8m.
Previously, the only shareholders were chief executive and founder Roger Norwich and his wife, Jane Norwich.
The company, which became a plc on Monday, is thought to be the only company that employs doctors full time to investigate claimaints' medical history and write medical reports.
Norwich said MLC had just over 1% of a market estimated to be worth between £350m and £500m. There are said to be 1.8 million accidents a year leading to personal injury claims.
The Ofex listing would boost MLC's profile and allow it to launch a share option scheme that could be worth about a year's salary for longer serving staff.
MLC has grown from employing about 15 doctors a year ago to 24 now, with 35 support staff.
Norwich said the market for MLC's services took a knock in the wake of the Woolf reforms.
"Things did turn down for the medical report industry, but now that things have shaken down, it's going forward and we want to be there," he said.
Norwich said that insurers needed to fight off a growing number of personal injury claims.
"Personal injury is the thing for lawyers at the moment and many of them are setting up big professional indemnity departments. They'll be attacking insurers with claims.
"Not all the claims will be as reasonable as they might have been five or ten years ago, so a company like ours is well placed to help insurers defend themselves."
He cited an example in which a claim for £25,000 was cut to £800, after it was shown that a medical report by a consultant orthopaedic surgeon was based on incomplete evidence.
"If you see a consultant's name on a report it looks impressive, but many of the reports are singularly unimpressive when you start to look at the details that have been missed," he said.